The Lakers and D'Antoni's agent, Warren LeGarie, confirmed the deal two days after the Lakers fired Brown five games into the season.
D'Antoni agreed to a three-year deal with a team option for a fourth season.
D'Antoni got the high-profile job running the 16-time NBA champions only after the club's negotiations broke down with former Lakers coach Phil Jackson. The 11-time NBA champion coach met with Lakers owners Jerry and Jim Buss and general manager Mitch Kupchak on Saturday to discuss a return for a third stint on Los Angeles' bench.
The Lakers' top brass instead went with D'Antoni, who coached Lakers point guard Steve Nash during five seasons in Phoenix. Nash won two MVP awards while running D'Antoni's signature up-tempo offense for the coach's final four seasons, when they won at least 54 games each season and reached two Western Conference finals.
D'Antoni then coached New York for the past four seasons, resigning last March after a largely unsuccessful tenure featuring just one playoff appearance and no postseason victories. D'Antoni also coached the Denver Nuggets during the lockout-shortened 1998-99 season.
Nash and Kobe Bryant both have expressed enthusiasm about the prospect of playing for D'Antoni, although Bryant also campaigned eagerly for Jackson.
D'Antoni underwent knee replacement surgery earlier this month and could be limited in his mobility and travel for the first few weeks of his tenure in Los Angeles, although the Lakers likely won't announce specifics until later in the week.
Jackson won five titles and reached seven NBA finals during two stints totaling 11 seasons with Los Angeles. He walked away from the club 18 months ago after a second-round playoff sweep by Dallas, and Brown led Los Angeles to a 41-25 mark and another second-round playoff defeat last summer.
The Lakers traded for Nash and Dwight Howard, setting up a season of enormous expectations for Brown - but the Lakers struggled to learn his new, Princeton-influenced offense while playing mediocre defense.
After the Lakers stumbled out of the gate while Howard and Bryant missed preseason games to preserve their health, Nash incurred a small fracture in his leg during the Lakers' second regular-season game, keeping him out of the lineup for their past five games and for at least another week.
The Lakers reached a deal with D'Antoni several hours after they beat Sacramento 103-90 for their second straight win under interim coach Bernie Bickerstaff.
The Lakers have improved to 3-4 after following up their winless preseason with four losses in their first five regular-season games, the club's worst start since 1993.
D'Antoni's reputation as an innovative coach wasn't helped by his tenure in New York, although he took over a moribund franchise and eventually returned it to respectability.
Despite his reputation for offensive acumen, D'Antoni's NBA teams typically have played fairly solid defense, statistically speaking - and they never had the imposing Howard or defensive stopper Metta World Peace in their lineups.
Nash had his best NBA seasons as the versatile quarterback of the Suns' offense under D'Antoni, and point guard Jeremy Lin became a star on the Knicks last season while filling much the same role. D'Antoni resigned late last season following a six-game losing streak, surprising many observers.
The Lakers' next game is Tuesday night against San Antonio. Phoenix visits Staples Center on Friday. From SI.com